Solution Manual for Mathematics for Electricity and Electronics, 4th Edition

Solutions Manual to Accompany MATHEMATICS FOR ELECTRICITY AND ELECTRONICS FOURTH EDITION Arthur D. Kramer Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Solutions Manual to accompany: Mathematics for Electricity and Electronics, Fourth edition Arthur D. Kramer Vice President, Editorial: Dave Garza Director of Learning Solutions: Sandy Clark  2012, 2006, 2002, 1995 Delmar, Cengage Learning ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher. Acquisitions Editor: Stacy Masucci Managing Editor: Larry Main Product Manager: Mary Clyne Vice President, Marketing: Jennifer Baker Marketing Director: Deborah Yarnell Marketing Manager: Erin Brennan For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Further permissions questions can be e-mailed to [email protected] Production Director: Wendy Troeger Production Manager: Mark Bernard ISBN-13: 978-1-1115-4513-0 Content Project Manager: Glenn Castle Art Director: David Arsenault ISBN-10: 1-1115-4513-8 Delmar 5 Maxwell Drive Clifton Park, NY 12065-2919 USA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at: international.cengage.com/region Cengage Learning products are represented in Canada by Nelson Education, Ltd. To learn more about Delmar, visit www.cengage.com/delmar Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com Notice to the Reader Publisher does not warrant or guarantee any of the products described herein or perform any independent analysis in connection with any of the product information contained herein. Publisher does not assume, and expressly disclaims, any obligation to obtain and include information other than that provided to it by the manufacturer. The reader is expressly warned to consider and adopt all safety precautions that might be indicated by the activities described herein and to avoid all potential hazards. By following the instructions contained herein, the reader willingly assumes all risks in connection with such instructions. The Publisher makes no representations or warranties of any kind, including but not limited to, the warranties of fitness for particular purpose or merchantability, nor are any such representations implied with respect to the material set forth herein, and the publisher takes no responsibility with respect to such material. The publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or part, from the readers’ use of, or reliance upon, this material. Contents CHAPTER 1 Basic Arithmetic Arithmetic Operations Exercise 1.2 Exercise 1.3 Multiplying and Dividing Fractions 1 Adding Fractions 2 Exercise 1.4 Hand Calculator Operations 2 Review Exercises CHAPTER 2 1 Exercise 1.1 1 3 Decimals and Percentages Exercise 2.1 Decimals 3 3 Exercise 2.2 Percentages 4 Exercise 2.3 Precision and Accuracy 5 Exercise 2.4 Hand Calculator Operations 5 Review Exercises 6 CHAPTER 3 Powers and Roots Exercise 3.1 Exercise 3.2 Powers 6 Powers of Ten 6 7 Exercise 3.3 Square Roots and Cube Roots 8 Exercise 3.4 Hand Calculator Operations 8 Review Exercises 9 CHAPTER 4 Systems of Measurement Exercise 4.1 Exercise 4.2 10 Scientific and Engineering Notation Metric System (SI) 11 10 Exercise 4.3 The U.S. Customary System 12 Exercise 4.4 Hand Calculator Operations 13 Review Exercises 14 CHAPTER 5 Basic Algebra 15 Exercise 5.1 Signed Numbers 15 Exercise 5.2 Algebraic Terms 15 Exercise 5.3 Rules for Exponents 16 Review Exercises 17 CHAPTER 6 Linear Equations 18 Exercise 6.1 Solution of First-Degree Equations 18 Exercise 6.2 Equation Solving Methods 19 Review Exercises 19 CHAPTER 7 Basics of DC Circuits Exercise 7.1 DC Circuits and Ohm’s Law 20 20 iii iv • CONTENTS Exercise 7.2 Electric Power Review Exercises CHAPTER 8 Multiplying and Factoring Polynomials Exercise 8.1 Multiplying Polynomials Exercise 8.2 Exercise 8.3 Monomial Factors 23 Binomial Factors 24 Exercise 8.4 Second-Degree Equations 24 Review Exercises CHAPTER 9 21 22 22 22 25 Algebraic Fractions 26 Exercise 9.1 Reducing Fractions 26 Exercise 9.2 Exercise 9.3 Multiplying and Dividing Fractions 26 Addition of Fractions 27 Exercise 9.4 Equations with Fractions 28 Review Exercises 29 CHAPTER 10 Formulas and Problem Solving Exercise 10.1 Exercise 10.2 Review Exercises CHAPTER 11 33 Series and Parallel DC Circuits Exercise 11.1 Exercise 11.2 34 Series Circuits 34 Parallel Circuits 35 Exercise 11.3 Series-Parallel Circuits Review Exercises 37 CHAPTER 12 31 Formulas and Literal Equations 31 Problem Solving 32 36 Graphs Exercise 12.1 Exercise 12.2 39 Rectangular Coordinate System Linear Function 42 39 Exercise 12.3 Nonlinear Graphs 46 Review Exercises 50 CHAPTER 13 Linear Systems 54 Exercise 13.1 Graphical Solution of Two Equations 54 Exercise 13.2 Algebraic Solution of Two Equations 56 Exercise 13.3 Solution by Determinants 57 Exercise 13.4 Solution of Three Linear Equations 58 Review Exercises 59 CHAPTER 14 Network Analysis Exercise 14.1 Voltage Division 60 Exercise 14.2 Kirchhoff’s Laws 61 Exercise 14.3 Solving Circuits 61 Review Exercises 62 60 CONTENTS CHAPTER 15 Network Theorems CHAPTER 16 Superposition Theorem Exercise 15.2 Exercise 15.3 Thevenin’s Theorem 64 Norton’s Theorem 66 CHAPTER 17 63 67 Trigonometry of the Right Triangle Exercise 16.1 Angles and Triangles Exercise 16.2 Exercise 16.3 Pythagorean Theorem 70 Trigonometric Ratios 70 Review Exercises 69 69 71 Trigonometry of the Circle Exercise 17.1 72 Trigonometric Functions 72 Exercise 17.2 Reference Angles and Special Angles Exercise 17.3 Inverse Functions 73 Review Exercises 74 CHAPTER 18 73 Alternating Current Exercise 18.1 Exercise 18.2 v 63 Exercise 15.1 Review Exercises • 75 Alternating Current Waves 75 Root Mean Square Values 77 Exercise 18.3 Frequency and Period 78 Exercise 18.4 Phase Angle 79 Review Exercises 81 CHAPTER 19 Trigonometry of Vectors Exercise 19.1 Exercise 19.2 Exercise 19.3 Law of Cosines Review Exercises 84 CHAPTER 20 82 Vectors and Phasors Law of Sines 83 82 83 Complex Numbers and Phasors Exercise 20.1 The j Operator 85 Exercise 20.2 Complex Numbers 85 Exercise 20.3 Complex Phasors 86 Exercise 20.4 Operations with Complex Phasors Review Exercises 89 CHAPTER 21 85 88 Series AC Circuits 90 Exercise 21.1 Inductive Reactance and RL Series Circuits 90 Exercise 21.2 Capacitive Reactance and RC Series Circuits 91 Exercise 21.3 RLC Series Circuits and Resonance 92 Review Exercises 93 CHAPTER 22 Parallel AC Circuits Exercise 22.1 Exercise 22.2 RL Circuits 94 RC Circuits 94 94 vi • CONTENTS Exercise 22.3 Susceptance and Admittance Exercise 22.4 Exercise 22.5 RLC Circuits 96 AC Networks 97 Exercise 22.6 Filters Review Exercises CHAPTER 23 97 98 Exponents and Logarithms 99 Exercise 23.1 Fractional Exponents 99 Exercise 23.2 Exercise 23.3 Exponential Functions 100 Common and Natural Logarithms Review Exercises CHAPTER 24 95 102 103 Applications of Logarithms Exercise 24.1 104 Exponential Equations 104 Exercise 24.2 RC and RL Circuits 105 Exercise 24.3 Power and Gain 106 Exercise 24.4 Bode Plots 107 Review Exercises 116 CHAPTER 25 Computer Number Systems Binary Number System 119 Binary Arithmetic 119 Exercise 25.3 Exercise 25.4 Exercise 25.5 Octal Number System 120 Hexadecimal Number System 121 Hexadecimal Arithmetic 121 Exercise 25.6 Computer Codes Review Exercises 122 CHAPTER 26 119 Exercise 25.1 Exercise 25.2 122 Boolean Algebra 124 Exercise 26.1 Boolean Algebra 124 Exercise 26.2 Logic Circuits 125 Exercise 26.3 Karnaugh Maps 126 Review Exercises 127 CHAPTER 27 Statistics Exercise 27.1 Mean, Median, and Mode 128 Exercise 27.2 Standard Deviation 129 Exercise 27.3 Histograms and the Normal Curve 130 Review Exercises 132 128 Detailed solutions are shown for more difficult problems. For a group of similar problems, procedures are shown for the first one in the group and for any others that differ significantly. CHAPTER 1 Basic Arithmetic Exercise 1.1 Arithmetic Operations $640 = $16/hr; 40 $570 teacher = $19/hr 30 1. 16 16. 14 31. 1 2. 15 17. 77 32. 1 3. 4 18. 9 33. 10 4. 20 19. 45 34. 19 5. 120 20. 200 35. 55 45. (6000)(9000) = 54,000,000 mi 6. 160 21. 10 36. 150 46. 7. 4 22. 250 8. 57 23. 2 9. 36 24. 30 10. 7 11. 40 25. 120 26. 40 37. 1500 38. 510 39. 1 40. 5 41. 3 42. 5 12. 5 27. 5 13. 50 28. 5 14. 2 29. 25 15. 26 30. 9 Exercise 1.2 43. 180 = 20 mi/gal; 90 44. tech 44 km = 22 km/h 2h 47. 1 A 48. 2 A 49. 16 V 50. 12 V 51. 7 52. 122 210 = 21 mi/gal 10 Multiplying and Dividing Fractions 1. 35 6 12. 13 2. 13 9 13. 35 23. 25 34. 18 1 24. 12 35. 6 28 45 36. 3 3. 45 14. 17 25. 4. 12 2 15. 15 26. 10 11 37. 13 5. 43 1 16. 24 27. 2 38. 15 6. 23 4 17. 15 1 28. 45 39. 12 7. 15 18. 11 60 29. 165 40. 25 30. 11 12 41. 8 1 8. 20 9. 2 9 19. 43 20. 6 31. 5 6 42. 145 10. 37 21. 2 5 32. 21 43. 6 2 11. 11 22. 5 2 33. 21 44. 32 1 • 2 CHAPTER 1 Basic Arithmetic 45. 1 46. 4 15 3 ft 47. = 50 10 3 48. (100) = 75 ft 4  3  1  49. (1000)     = $300  5  2  1  1 50. ( 40,000)     = $5000  2  4 51. 27 V 1 A 53. 16 1 A 54. 50 9 W 55. 25 52. 60 V 1 W 56. 20 1. 77 = 1 24. 69 35 41 47. 100 2. 45 25. 5 1 48. 50 3. 85 26. 43 49. 11 20 4. 65 33 27. 80 50. 43 5. 13 20 37 28. 100 51. 83 11 6. 14 29. 127 200 52. 14 7. 19 24 49 30. 120 33 53. 40 8. 11 12 7 31. 20 9. 14 15 7 32. 100 10. 25 63 33. 100 31 11. 60 34. 15 4 31 12. 36 31 35. 60 57 13. 200 7 36. 24 14. 41 75 37. 23   1  60. (5 ft 3 in) − (6)  in  ÷ 5 = 1 ft  2   15. 14 38. 65 61. 10 Ω 1 16. 10 7 39. 12 17. 16 6 40. 25 1 18. 60 1 41. 80 19. 9 10 42. 59 100 20. 7 8 43. 13 12 Exercise 1.3 Adding Fractions 54. 25 55. 1 lb 56. up 85 lb 57. 14 58. 18 59. 13 in 4 62. 25 Ω 63. 20 Ω 64. 300 Ω 65. 20 Ω 3 66. 40 Ω 3  1    1    20 67.   3 ÷      = 4 10    2    3  21. 11 20 3 44. 20 1 22. 20 45. 14 15 85 23. 24 46. 83 9 7 68. 10   = 9  20  20 1. 4 4. 1900 7. 412 2. 197 5. 130 8. 4 3. 47 6. 12 9. 2 Exercise 1.4 7 10 Hand Calculator Operations Exercise 2.1 10. 3 17. 1 24. 1 11. 147 18. 2 25. 710 (OIL) 12. 32 19. 1 13. 60 20. 1 14. 3 21. 4 15. 40 22. 2 16. 200 23. 12 Decimals 26. 142857 27. 666.7 Ω 28. 57.1 Ω Review Exercises 1. 22 20. 17 6 40. 500 − 400 − 25 = $75 2. 47 21. 2 41. 1000 + 250 = $1250 3. 12 22. 2 4. 400 7 23. 24   3  4 42. 7 − 15  ÷ 12 ÷ 16 = ft   5 8   5. 21 24. 13 40 6. 135 5 25. 36 1 A 44. 16 7. 15 4 26. 25 45. 10 V 27 27. 100 8. 12 28. 9. 32 29. 10. 25 30. 11. 15 2 1 28 8 7 7 16 31. 200 12. 19 32. 58 13. 4 33. 147 14. 10 34. 2 43. 12 A 46. 24 V 5 47. 185 W 48. 24 W 49. 27 V 50. 25 A 51. 20 Ω 52. 60 Ω 15. 52 35. 2 53. 20 Ω 16. 45 36. 3 54. 37 Ω 11 17. 16 37. 25 mi/h 55. 38. $160 1 18. 50  1 39.   (500) = 250 ft  2 19. 15 56. 1  3  5  25 5 ÷    = 5  5   3 9 e 207 je12 j 9 10 CHAPTER 2 Decimals and Percentages Exercise 2.1 Decimals 1. 10.09 5. 22.71 9. 0.0062 2. 65.129 6. 7.39 10. 10.01 3. 0.91 7. 4.05 11. 12 4. 69.384 8. 1.202 12. 0.069 = 7 36 • 3 4 • CHAPTER 2 Decimals and Percentages 13. 6.25 24. 2.8 35. 10 44. 3.12 cm 14. 0.02804 25. 32 36. 1000 45. 0.5555 cm2 15. 0.00001 26. 50 37. 40 46. 0.08 in, 0.0004 in2 16. 0.00006 27. 0.8 38. 0.55 47. 8.4 ft 17. 30 28. 1.612 39. 7 48. 109.72 m 18. 210 29. 12.3 40. 0.3 49. 40.1 V 19. 0.12 30. 0.87 41. 0.08 50. 1.50 A 20. 33.01 31. 0.02 42. 0.4 51. 17.0 cm 21. 10 32. 0.15 43. 0.2083 mm 52. 4.4 mm, 1.21 mm2 22. 0.1 33. 4 23. 0.08 34. 0.121 Exercise 2.2 Percentages 1. 0.75, 75% 7 , 0.35 22. 20 17 , 0.085 43. 200 64. 30 g 2. 0.5, 50% 23. 24. 1 , 0.0625 16 1 , 0.1% 1000 65. 85% 3. 0.4, 40% 4. 0.3, 30% 25. 5. 0.375, 37.5% 26. 43 , 0.86 50 11 , 0.55 20 99 , 0.99 100 49 , 0.49 100 6. 0.875, 87.5% 44. 45. 66. 0.025% 46. 0.002, 0.2% 67. $38.00, $42.75 47. 3 68. $44.00 27. 0.05, 5% 48. 16 69. $64.00, $68.80 7. 0.04, 4% 28. 0.12, 12% 49. 15 70. $20.00, $21.65 8. 0.09, 9% 29. 1.25, 125% 50. 30 71. $42.00, $44.10 9. 0.5625, 56.25% 30. 2.4, 240% 51. 1.35 72. $642 52. 1.19 73. 12% 53. 75 74. 20% 54. 12.5 75. 110%, 1120 , 9 , 1 1 , 1.19 1000 8 6 55. 81 1, 76. 0.03, 40 , 0.50% 25 56. 12 77. 165 Ω 57. 1.65 78. 532 Ω 58. 0.4875 79. 0.11 A, 1.21 A 59. 2.5 80. 0.22 A, 0.88 A 39. 33%, 0.33 60. 3.625 81. 40% decrease 40. 0.0625, 6.25% 61. $13.20 82. 50% increase 41. 163 , 18.75% 62. $150.00 83. 20% increase 42. 87 , 87.5% 63. 0.95 ft3 84. 25% decrease 10. 0.15, 15% 31. 3 11. 15%, 20 32. 25%, 14 1 10%, 10 60%, 35 3 12%, 25 4 16%, 25 7 28%, 25 9 36%, 25 1 , 0.2 5 4 , 0.8 5 3 , 0.15 20 33. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 34. 35. 36. 37. 38. 1 , 5% 20 2 , 8% 25 3, 150% 2 1, 100% 1 6 , 1.2 5 2, 2.0 1 7 , 0.056 125 101 , 0.505 200 0. 5 Exercise 2.4 Exercise 2.3 Hand Calculator Operations Precision and Accuracy 1. 3 22. 3 43. 1000, 1000, 999 2. 3 23. 5, 5.2, 5.15 44. 9000, 8900, 8890 3. 2 24. 3, 3.1, 3.10 45. 461 m2 4. 2 25. 300, 320, 318 5. 3 26. 100, 120, 121 6. 4 27. 0.4, 0.44, 0.445 7. 3 28. 0.4, 0.44, 0.440 48. 27.1 ft/s, 18.5 mi/h 8. 1 29. 10,000, 9900, 9910 49. 18 V 9. 4 30. 10,000, 11,000, 10,900 50. 30 mA 10. 1 31. 80,000, 82,000, 81,900 11. 4 32. 1000, 1100, 1070 12. 3 33. 100, 100, 101 13. 4 34. 30, 29, 29.0 53. 120 V 14. 1 35. 20, 19, 18.9 54. 0.11 A 15. 4 36. 0.09, 0.090, 0.0899 55. 1480 W 16. 3 37. 20, 20, 20.0 17. 4 38. 40, 39, 39.1 56. (a) 1.3 Ω (b) 1.28 Ω 18. 2 39. 300, 340, 336 19. 2 40. 500, 450, 454 20. 4 41. 300, 260, 260 21. 4 42. 700, 680, 678 58. (a) $170 (b) $172 1. 2 15. 0.143 29. 0.00266 2. 8280 16. 0.75 30. 20.7 3. 21.1 17. 0.860 31. 197,000,000 mi2 4. 950 18. 2.69 32. 14.9 cm 5. 2.0 19. 35.5 6. 3 20. 124 33. (a) 4.67% (b) 19.1% 7. 0.5 21. 1.90 8. 2.5 22. 167,000 9. 147 23. 110 10. 48.4 24. 505 11. 2.4 25. 8.27 12. 0.20 26. 0.0270 13. 0.68 27. 0.00482 14. 0.00844 28. 0.000900 Exercise 2.4 • 46. 5,570,000 m3 47. 152 lb 51. 203 in2 52. 0.046 cm3 57. (a) $43 (b) $46 Hand Calculator Operations . ) + (7,850)(0.029) 34. (87,000)(0153 = $13,538.65 35. 33.0 V 36. 295 V 37. 0.415 A 38. 0.338 A 5 6 • CHAPTER 3 Powers and Roots Review Exercises 1. 31.26 22. 18 , 0.125 43. 66.9 2. 0.0011 11 , 0.055 23. 200 44. 149 9 , 0.9% 1000 3. 4.04 24. 4. 8.464 25. 0.005, 0.5% 5. 220.1 26. 3, 1.5 2 6. 30 27. 1 7. 0.25 28. 8 8. 4 29. 8.4 9. 0.006 30. 24.5 10. 0.144 31. 39 11. 20 32. 0.9 12. 0.025 33. 82.5 13. 44 34. 8.55 14. 0.01 35. 0.5 15. 0.8, 80% 36. 51 16. 0.125, 12.5% 37. 33 17. 0.15, 15% 38. 3.4 18. 103 , 30% 39. 0.95 4 , 16% 19. 25 40. 0.058 20. 2, 200% 41. 31.0 7 , 0.35 21. 20 42. 0.867 45. 25.3 in, 26.7 in2 46. $1317.50, $1240.00 47. (40,000)(0.4)e 43 j = $12,000 48. (317)(10)(0.75) = 2380 Btu/h 49. $59.84, $64.33 50. $110 51. 76 52. 0.0048 s 53. (a) 0.41 A (b) 2.5 A 54. 210 Ω 55. 10% 56. 33% 57. (4700)e13 j(0.75) = 1175 ≈ 1200 Ω 58. 0.41 A 59. 21 mA 5 (100%) = 33% 60. (a) 15 (b) 2.5/ e 23 j = 167 . ≈ 1.7 Ω CHAPTER 3 Powers and Roots Exercise 3.1 Powers 1. 81 1 , 0.008 12. 125 22. 18 , 0.125 2. 64 13. 10 ,1000 , 0.0001 23. 0.0001, 10 ,1000 49 , 0.49 14. 100 1 , 0.0016 24. 625 25, 1.5625 15. 16 25. 0.000008, 1251, 000 81 , 0.1296 16. 625 27 26. 0.027, 1000 7. 121 9 17. 0.36, 25 27. 19 , 0.111 … 8. 8000 1 18. 0.008, 125 28. 50 1 , 0.0625 9. 16 19. 2.25, 94 29. 1 27 , 0.027 10. 1000 20. 36 , 1.44 25 30. 75, 1.4 9 , 0.36 11. 25 8 , 0.064 21. 125 1 , 0.025 31. 40 3. 128 4. 125 5. 100,000 6. 625 Exercise 3.2 Powers of Ten 32. 12 , 2.4 5 1 , 0.002 43. 500 54. 8100 ft2 6 , 0.048 33. 125 8 , 0.32 44. 25 55. $26,620 34. 14 , 0.25 5 = 0.078125 45. 64 56. $140.26 35. 18 , 0.125 3 , 0.024 46. 125 57. 2.25 mm2 67 , 0.067 36. 1000 17 , 0.068 47. 250 58. 0.396 ft3 1 , 0.05 37. 20 21 , 1.05 48. 20 59. 20 Ω 11 , 0.11 38. 100 , 18.75 49. 75 4 60. 125 Ω , 52.25 50. 209 4 61. 17 W 51. 19 , 0.111 … 62. 50.7 W 1 , 0.0625 52. 16 63. 0.06 W 53. 0.512 cm3 64. 18 W 1. 103 23. 0.000001, 1, 0001, 000 46. 10 −6 2. 106 1 24. 0.000000001, 1, 000 , 000 , 000 39. 25 , 3.125 8 40. 144 , 5.76 25 41. 9 , 0.18 50 729 , 7.29 42. 100 Exercise 3.2 Powers of Ten 47. 10 −1 3. 100 25. 10 48. 10 −4 4. 109 26. 1000 49. 104 5. 10 −6 27. 106 50. 107 6. 10 −3 28. 109 51. 102 7. 10 −4 29. 10 −5 52. 100 = 1 8. 10 −1 30. 10 −10 53. 10 −3 9. 10 −2 31. 10 −6 54. 10° = 1 10. 10 −5 32. 10 −1 55. 109 11. 10 −1 33. 109 56. 10−6 12. 10 −3 34. 106 57. 10 −1 13. 10 −3 35. 10 −9 58. 10 −8 14. 10 −4 36. 100 59. 12 × 102 15. 100,000 37. 103 60. 49 × 100 = 49 16. 100,000,000 38. 104 61. 24 × 101 = 24 × 10 17. 1,000,000 39. 10−2 62. 72 × 102 18. 1 40. 10−5 63. 6 × 10−12 41. 101 = 10 64. 45 × 10 −4 42. 102 65. 12 × 10 −1 43. 10−2 66. 4 × 106 44. 10−6 67. 3 × 103 45. 102 68. 5 × 10 −3 1 19. 0.01, 100 20. 0.0001, 10 ,1000 21. 1 0.1, 10 1 22. 0.001, 1000 • 7 • 8 CHAPTER 3 Powers and Roots 77. 7 × 10 −9 , 0.000000007 69. 2.5 × 107 70. 5 × 10 7 71. 2.5 × 10 78. 5 × 1012, 5,000,000,000,000 −2 79. 72. 4.5 × 105 73. 0.75 × 106 74. 1 × 105 75. 16 × 103, 16,000 76. 40 × 10 −6 , 0.000040 Exercise 3.3 6.5 × 104 , 65 × 10 , 3 65,000 80. 6 × 103 = 60 × 102 = 6000 81. 29 × 10 −4 = 2.9 × 10 −3 , 0.0029 82. 43 × 10−2 = 4.3 × 10 −1 , 0.43 89. 3.0 V 90. 0.0099 V 83. 4.5 × 10 = 45 91. 0.05 A 84. 0 92. 0.11 A 85. 480 W 93. 2000 Ω 86. 3.8 W 94. 300,000 Ω 87. 45.5 A 88. 100 A Square Roots and Cube Roots 1. 4 23. 0.1 45. 16 × 108 68. 0.32 × 10 −2 2. 11 24. 0.2 46. 27 × 1012 69. 0.75 × 105 3. 52 25. 10 47. 0.64 × 1010 70. 4 × 102 4. 103 26. 0.1 48. 0.01 × 102 71. 70 ft 2 3 2 9 27. 14 49. 0.001 × 109 28. 18 50. 0.008 × 1018 7. 0.8 29. 28 51. 9 × 1011 8. 0.6 30. 24 52. 32 × 1010 9. 0.1 31. 1.4 53. 150 × 106 10. 0.3 32. 2.2 11. 200 33. 2.1 12. 50 34. 1.8 13. 30 35. 12 14. 40 36. 18 15. 0.09 37. 0.6 = 35 5. 6. 54. 0.2 × 1014 55. 4 × 103 1 0.04 = 25 72. 100 mm, 10 cm 73. 3% 74. 4% 75. 2.5 76. 0.1 ft 77. 20 Ω 56. 5 × 102 78. 25 Ω 57. 12 × 10 79. 60 V 58. 7 × 106 80. 0.02 A 59. 0.5 × 102 81. 0.2 A 60. 0.8 × 103 82. 48 V 16. 0.12 38. 61. 2 × 103 17. 1.3 83. 6.4 W 39. 2 62. 3 × 10 18. 1.5 40. 15 = 0.2 84. 7.2 W 63. 6 × 10 19. 3 1 41. 0.1 = 10 64. 5 × 104 20. 5 42. 12 = 0.5 65. 0.2 × 10 3 85. 0.05 A 86. 400 V 1 16 2 + =2 9 9 21. 12 43. 64 × 10 9 66. 0.5 × 10 −1 87. 22. 25 44. 36 × 104 67. 1.5 × 10 −5 88. 4(9) − 11 = 25 Exercise 3.4 Hand Calculator Operations 1. 58.1 3. 0.0101 5. 0.655 7. 79.7 2. 0.885 4. 56.6 6. 0.0364 8. 8.95 Review Exercises 9. 0.242 16. 0.606 23. 0.794 W 10. 2.95 17. 57.4 24. 1320 W 11. 57.0 18. 2.19 25. 4830 Ω 12. 0.202 19. 97.9 26. 9.66 × 10 3 Ω 13. 15.0 20. 2.74 14. 0.940 21. 148 cm3 15. 10.1 22. 341 m/s Review Exercises 1. 343 3 27. 0.06, 50 53. 1 × 108 2. 121 9 28. 0.9, 10 54. 10 1 , 0.0625 3. 16 8 , 0.064 4. 125 27 5. 0.216, 125 6. 7. 8. 8 0.064, 125 121 1.21, 100 1 0.001, 1000 1 9. 0.01, 100 10. 0.625, 85 11. 25, 0.4 1 12. 0.004, 250 13. 1 14. 18 , 0.125 29 15. 0.29, 100 1 16. 0.0625, 16 17. 7 18. 65 , 1.2 19. 25, 0.4 31. 22. 23. 4 24. 0.3, 103 57. 6.5 × 103 = 65 × 102 7, 1.4 5 58. 12 × 10 −6 = 120 × 10 −7 9 32. 0.9, 10 59. 81 × 108 33. 100,000,000 60. 6.75 × 106 34. 0.00001, 1001, 000 61. 9 × 103 35. 10 ,1000 , 0.0001 36. 103 = 1000 37. 102 = 100 38. 10 −6 = 0.000001, 1, 0001, 000 62. 0.6 × 10 63. 4 × 103 64. 0.2 × 102 65. 7 × 103 66. 9 × 102 39. 104 = 10,000 67. 0.1 × 107 40. 10 −4 = 0.0001, 10 ,1000 68. 0.8 × 102 41. 10 −5 = 0.00001, 1001, 000 69. 0.0140 1 42. 10 −1 = 0.1, 10 70. 0.0301 43. 109 = 1,000,000,000 1 44. 10 −1 = 01 . , 10 45. 106 = 1,000,000 46. 10 11 0.11, 100 56. 1 × 10 −6 30. 11 20. 2 21. 0.3, 103 55. 16 × 105 29. 7 −6 = 0.000001, 1, 0001, 000 47. 14 × 102 48. 24 × 10 −8 49. 2 × 10 −3 50. 4.5 × 10 −1 71. 277 72. 0.308 73. 51.7 74. 0.136 75. 9.48 76. 0.326 77. 56 ft 78. $102.50 79. 50 mm = 5 cm 25. 1 51. 010 . × 10 −9 = 10 . × 10 −10 80. 0.216 m3 26. 13 52. 2.5 × 100 = 2.5 81. 50 Ω • 9